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RSB [31]
2 years ago
5

A chess club has 480 members but is losing 30 members each year. A computer club has 130 members and is gaining 20 members per y

ear. When will the two clubs have the same number of members?
Mathematics
1 answer:
Alexxandr [17]2 years ago
8 0

Answer:

The two clubs will have the same number of members after 7 years

Step-by-step explanation:

Let the number of years is x

∵ A chess club has 480 members but is losing 30 members each year

∵ The number of years = x

∴ The total members after x years = 480 - 30x ⇒ (1)

∵ A computer club has 130 members and is gaining 20 members per year

∵ The number of years = x

∴ The total members after x years = 130 + 20x ⇒ (2)

∵ The two clubs will have the same number of members after x years

→ Equate (1) and (2)

∴ 480 - 30x = 130 + 20x

→ Add 30x t both sides

∵ 480 - 30x + 30x = 130 + 20x + 30x

∴ 480 = 130 + 50x

→ Subtract 130 from both sides

∵ 480 - 130 = 130 - 130 + 50x

∴ 350 = 50x

→ Divide both sides by 50

∴ 7 = x

∴ The two clubs will have the same number of members after 7 years

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2 years ago
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 73 minutes and a standard devi
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Answer:

(a) X\sim N(\mu = 73, \sigma = 16)

(b) 0.7910

(c) 0.0401

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Step-by-step explanation:

Let <em>X</em> = amount of time that people spend at Grover Hot Springs.

The random variable <em>X</em> is normally distributed with a mean of 73 minutes and a standard deviation of 16 minutes.

(a)

The distribution of the random variable <em>X</em> is:

X\sim N(\mu = 73, \sigma = 16)

(b)

Compute the probability that a randomly selected person at the hot springs stays longer than 60 minutes as follows:

P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-73}{16})\\=P(Z>-0.8125)\\=P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that a randomly selected person at the hot springs stays longer than an hour is 0.7910.

(c)

Compute the probability that a randomly selected person at the hot springs stays less than 45 minutes as follows:

P(X

*Use a <em>z</em>-table for the probability.

Thus, the probability that a randomly selected person at the hot springs stays less than 45 minutes is 0.0401.

(d)

Compute the probability that a randomly person spends between 60 and 90 minutes at the hot springs as follows:

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*Use a <em>z</em>-table for the probability.

Thus, the probability that a randomly person spends between 60 and 90 minutes at the hot springs is 0.6464

6 0
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Answer:

The perimeter is 1280ft

Step-by-step explanation:

Let the side length of the square be s.

Then the distance around three sides is 3s.

According to the question the distance around 3 sides of a square city block is 960 feet.

This implies that:

3s = 960

s =  \frac{960}{3}

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Substitute s=320 to get:

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